The second-year forward out of Duke was hurt during an intrasquad scrimmage on Sunday, landing on a teammate's foot after going up for a rebound.
The team says he is expected to make a full recovery.
Bagley was averaging 14.2 points and 7.5 rebounds this season, but he has struggled to stay healthy, appearing in only 13 games.
The Kings are already without guard De'Aaron Fox, who is dealing with a left ankle sprain suffered last week. Buddy Hield, Harrison Barnes, Jabari Parker and Alex Len all tested positive for COVID-19 before training camp. A fifth player, center Richaun Holmes, inadvertently left the campus perimeter last week in Orlando, Florida, and had to go back into quarantine for 10 days.
After going 7-3 in its last 10 games before the March hiatus, Sacramento is 3½ games back of the Memphis Grizzlies for the No. 8 spot in the Western Conference.